# Finding Exact Value of Trig Expression

whatisphysics

## Homework Statement

Find the exact value of each expression:
a) sec-1($$\sqrt{}2$$)
b) sin-1(1)

## Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

## The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!

iamalexalright
These are inverse functions so:

a. For what value of x does sec(x) = sqrt(2)

b. For what value of x does sin(x) = 1?

Mentor

## Homework Statement

Find the exact value of each expression:
a) sec-1($$\sqrt{}2$$)
b) sin-1(1)

## Homework Equations

sec$$\theta$$=$$\stackrel{}{}1/cos\theta$$

## The Attempt at a Solution

I've never learned this, but I am really curious in how it is solved.
Is there a formula for this? Thanks!
Do you understand inverse functions?

IOW, x = f-1(y) <==> y = f(x)

For example, suppose you were asked to find cos-1(1/2).

Let y = cos-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

whatisphysics
Do you understand inverse functions?

IOW, x = f-1(y) <==> y = f(x)

For example, suppose you were asked to find cos-1(1/2).

Let y = cos-1(1/2).
That is equivalent to 1/2 = cos(y). What angle in the interval [0, $\pi$] has a cosine of 1/2?

Should I memorize the circle with all the angles?
And this may sound silly...but on (x,y), which is cos and sin? Is it like (cos, sin) on the circle, or the opposite?

Mentor
On the unit circle, x = cos(t) and y = sin(t).

Homework Helper
A simple way to look at the problem is let $$a=\sec^{-1}\sqrt{2}$$ then $$\sec a=\sqrt{2}$$. From here it is easy to compute the value a by turning sec into cos and using information about known values of cos.

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whatisphysics
Thank you all for the input! I think I will learn to memorize the circle with all the angles....I'm sure that will help.